A Dynamic Market Clearing Price Mechanism with Multiple Demands

Abstract

We propose a dynamic selling procedure for the generalization of the buyer-seller market game of Shapley and Shubik (1972) to the case where buyers can purchase more than one indivisible object, up to their quota, and have separable and additive utilities. This mechanism generalizes the auction studied by Demange et al. (1986), which in its turn is a generalization of the English auction to the multi-item case. It represents an enormous simplification of the restriction of the auction proposed by Gul and Stachetti (2000) to the linear case, by providing a different and simpler technique. Increasing the prices of all items of an overdemanded set chosen by the auctioneer always leads to the same price vector, namely the minimum competitive equilibrium price, in a finite number of steps. Consequently, the mechanism sells any two similar objects at the same price. When buyers are allowed to acquire the total amount of objects, the mechanism is strategy-proof.